The velocity-displacement graph of a particle is shown in Fig. 2 (EP). 10 . (a) Write the relationbetween (v) and (x).
(b) Obtain the relation between acceleration and displacement and plot it .
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Explanation

Refer Fig. 2. (EP). 11, 11, initial velocity` =v_0`, when ` t=0` Distance travelled in time ` t=x_0`. Let at an instant of time, the particle has velocity (v) and its displacement is (x0, which is located by position (A) on the graph.
Form graph, ` tan theta = V_0/X_0 = (v_0 -V0/x`
or ` (v_0x)/x-0 =v_0 -v or v=- v_0/x_0 x + v_0` ...(i)
Acceleration, ` a= (dv)/(dt) =- v_0/x_0 9sx)/(dt) + 0 =- v_0/x_0 [-v_0/x_0 x = v_0 ] ` [ from (i)]
or ` a= v_0^2/x_0^2 x - v_0^2/x_0`
Graph between (a) and (x) is shown in Fig.2 (EP).12.